A Note on the Stability of Solving a Rank- p Modification of a Linear System by the Sherman–Morrison–Woodbury Formula

In this paper, we address the stability of the Sherman–Morrison–Woodbury formula. Our main result states that if the original matrices, A and B, are well conditioned, then there exists matrices U and V such that the Sherman–Morrison–Woodbury formula is stable when applied to A = B - UVT.